Definition:Absolute Value of Mapping/Real-Valued Function
< Definition:Absolute Value of Mapping(Redirected from Definition:Absolute Value of Real-Valued Function)
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Definition
Let $S$ be a set.
Let $f: S \to \R$ be a real-valued function.
Then the absolute value of $f$, denoted $\size f: S \to \R$, is defined as:
- $\forall s \in S: \map {\size f} s := \size {\map f s}$
where $\size {\map f s}$ denotes the absolute value function on $\R$.
Absolute value thence is an instance of a pointwise operation on real-valued functions.
Also see
- Definition:Absolute Value of Mapping for the absolute value of more general mappings
- Definition:Pointwise Operation on Real-Valued Functions for other operations on real-valued functions